I have read all your posts OP, but only the first page of replies, so I apologise if I say something already covered.
Some blood tests can show whether it is more likely that you have a cancer or not. The ones that can do this won't necessarily be able to say what type of cancer you have, just that something unusual is going on.
The only way that they can be sure that your symptoms are not caused by a cancer is by looking at the area your symptoms suggest is the problem. In your case the only way they can do this is by at first inserting a finger a little way into your anus to see if they can feel anything obvious - they use lots of lubrication on their finger, it feels strange, and a little uncomfortable, but here are no sharp pains or anything. I was extremely embarrassed before having mine done, worrying about them getting a finger covered in faeces. We, as the patients, just have to face the embarrassment I am afraid. The Dr's are very used to doing this, they wear gloves, after all they chose this category of health care as their speciality. The Dr's face does not go near to your bottom to watch what he or she is doing, they will stay standing up while they do the digital (finger) exam by feel, so they certainly don't get a close up view of your genitals. It is nothing like where a medic has to peer into one's vagina for a smear test.
If the doctor could't tell by the digital exam whether it is one or more simple haemorrhoids causing your symptoms, he or she will make another appointment for you to have the last part of your large colon examined thoroughly, by using a very well lubricated tiny camera, inserted into your large colon, through your anus. As you describe you blood as bright red after having opened your bowels, he or she will almost certainly only have to examine the first part of the bowel that they come to through your anus. This is because if there is a problem higher up, the blood tends to be occult (occult only means hidden, it has no supernatural meanings at all). Occult blood may be observed by anyone who is examining faeces, seeing tarry looking stools, or just very dark to black stools. However, dark or tarry looking stools can be caused by lots of other things, including what you have eaten in the past few days. So anyone presenting with dark stools would be asked to collect some of them in a stool sample jar, which then needs to be examined under a microscope to see if it is in fact blood that it contains.
Anyway, I think you said that yours is red and flows more like a period. So like I said before, you probably won't have to have too much of your bowels examined. When I had this done - in a private facility, but paid for by the NHS - I was offered paper pants which have a convenient hole in them in the right place, and I was also offered I sedative.
They usually slip the sedative into a vein on the top of your hand, which only feels like a sharp prick (I know they are supposed to say scratch, but it always feels more like a prick to me!). The sedative doesn't actually send you to sleep, but it pleasantly relaxes you, and a lot of people afterwards can't remember anything about what procedure they just had. Again the doctor doesn't stay down by your bottom, he will probably be sitting down on a stool, but he will be watching what just looks like a TV screen, situated somewhere above you. He does not need to look at your bottom, but he does have to concentrate on the screen. If he doesn't see anything questionable, or some sore looking areas, he will probably give you the all clear, if he does see something that might be of some concern he will take a quick biopsy.
Unfortunately OP, the only way he or any other Dr or scientist, etc can tell for certain if you have a cancer is by doing these tests. Even private practitioners will not do more tests than are actually needed. Please go for whatever tests are advised OP, if they turn out to be negative, rejoice at that outcome, don't feel hard done by because you had them in the first place. Your severe embarrassment is understandable, to let it stop you having any advised tests is not.
Before you go for your endoscopy (I am just calling it that as I can't be certain how much of your bowels they will need to examine) you will probably have to take a rather disgusting drink for 2 to 3 days beforehand to clean your bowels (so that the camera can see all of its surface). It is not a bitter taste as such, it is more an unpleasant taste and texture, but that might well have improved in recent years.